Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use the clues to colour each square.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
How many trains can you make which are the same length as Matt's, using rods that are identical?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
How many different triangles can you make on a circular pegboard that has nine pegs?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
What is the best way to shunt these carriages so that each train
can continue its journey?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How many triangles can you make on the 3 by 3 pegboard?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An activity making various patterns with 2 x 1 rectangular tiles.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.